He quit without giving notice, you don't have to write shit. Beware, if he uses you as a reference I think it's illegal to say anything negative about him other than the fact that he worked for you during the period he claims.
Definitely suit up and pretend it's going to be an interview. If it turns out to be a friendly chat, no problem.
What do you mean by bring references? You should know who your references are but if the asks you for phone #s you can give them to him afterwards. Usually in the US people don't write references' contact information on their resumes.
Depends how coveted your internship is and therefore what caliber interns you can get.
Top tier financial institutions can get interns that basically do the same work as their first year analysts. If you're a tiny company with no rep then you'd probably only attract middling interns from state schools that require a ton of training.
If you comb through a thick stack of resumes and find some star interns you could load them up with some decently useful projects.